{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ReinforcementLearningAnIntroduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just like what we do in `Chapter03_Grid_World`, we need to create an environment model for the car rental problem. The only difference is that now it is a distributional environment model, which means given an action under certain state the model will return all the possible reward, next state together with the probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: redefining constant CarRentalEnvModel\n"
     ]
    }
   ],
   "source": [
    "using Distributions\n",
    "\n",
    "const PoissonUpperBound = 10\n",
    "const MaxCars= 20\n",
    "const MaxMoves = 5\n",
    "const CostPerMove = 2\n",
    "const CarRentalCartesianIndices = CartesianIndices((0:MaxCars,0:MaxCars))\n",
    "const CarRentalLinearIndices = LinearIndices((0:MaxCars,0:MaxCars))\n",
    "const Actions = -MaxMoves:MaxMoves\n",
    "const RequestDist_1 = Poisson(3)\n",
    "const RequestDist_2 = Poisson(4)\n",
    "const ReturnDist_1 = Poisson(3)\n",
    "const ReturnDist_2 = Poisson(2)\n",
    "\n",
    "decode_state(s::Int) = Tuple(CarRentalCartesianIndices[s])\n",
    "encode_state(s1::Int, s2::Int) = CarRentalLinearIndices[CartesianIndex(s1+1, s2+1)]\n",
    "decode_action(a::Int) = a - MaxMoves - 1\n",
    "encode_action(a::Int) = a + MaxMoves + 1\n",
    "\n",
    "\"reduce calculation\"\n",
    "function merge_prob(dist)\n",
    "    merged = Dict()\n",
    "    for (s′, r, p) in dist\n",
    "        if haskey(merged, (s′, r))\n",
    "            merged[(s′, r)] += p\n",
    "        else\n",
    "            merged[(s′, r)] = p\n",
    "        end\n",
    "    end\n",
    "    [(nextstate=s′, reward=r, prob=p) for ((s′, r), p) in merged]\n",
    "end\n",
    "\n",
    "function nextstep(state::Int, action::Int)\n",
    "    (s1, s2), a = decode_state(state), decode_action(action)\n",
    "    move = a > 0 ? min(a, s1) : max(a, -s2)\n",
    "    reward = -CostPerMove*abs(move)\n",
    "    s1′, s2′ = min(s1 - move, MaxCars), min(s2 + move, MaxCars)\n",
    "    merge_prob((nextstate = encode_state(min(max(s1′-req_1, 0)+ret_1, MaxCars), min(max(s2′-req_2, 0)+ret_2, MaxCars)),  # cars returned today can only be used in the next day\n",
    "                reward    = reward + (min(s1′, req_1) + min(s2′, req_2)) * 10,\n",
    "                prob      = pdf(RequestDist_1, req_1) * pdf(RequestDist_2, req_2) * pdf(ReturnDist_1, ret_1) * pdf(ReturnDist_2, ret_2))\n",
    "                for req_1 in 0:PoissonUpperBound, req_2 in 0:PoissonUpperBound, ret_1 in 0:PoissonUpperBound, ret_2 in 0:PoissonUpperBound)\n",
    "end\n",
    "\n",
    "const CarRentalEnvModel = DeterministicDistributionModel([nextstep(s, a) for s in 1:(MaxCars+1)^2, a in 1:length(Actions)]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can apply the `policy_iteration!` method to get the final value estimation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: replacing module BlackJack.\n"
     ]
    }
   ],
   "source": [
    "V, p = TabularApproximator(n_state=(1+MaxCars)^2), TabularDeterministicPolicy(zeros(Int,21^2), length(Actions))\n",
    "policy_iteration!(;V=V, π=p, model=CarRentalEnvModel, γ=0.9, max_iter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "ename": "ErrorException",
     "evalue": "type Irrational has no field table",
     "output_type": "error",
     "traceback": [
      "type Irrational has no field table",
      "",
      "Stacktrace:",
      " [1] getproperty(::Irrational{:π}, ::Symbol) at ./Base.jl:20",
      " [2] top-level scope at In[17]:1"
     ]
    }
   ],
   "source": [
    "heatmap(0:MaxCars, 0:MaxCars, reshape([decode_action(x) for x in π.table], 1+MaxCars,1+MaxCars))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heatmap(0:MaxCars, 0:MaxCars, reshape(V.table, 1+MaxCars,1+MaxCars))"
   ]
  }
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